Ok, based on one of the videos above, I found a inclinometer for my cell phone.
I've got a few different slopes around here. One hill is around 15° plus or minus a little. I can generally find flatter areas at the top and bottom for maneuvering.
I try to avoid mowing it, but it has been mowed some with a variety of machines. Parts of it has a bit of a compound slope (based on orientation), but I try to avoid driving cross slope.
My Ford 1715 tractor with AG tires will drive up and down just fine. I have all 4 tires set to their widest setting. I've also mowed with a smaller John Deer rider which was OK.
My Toro 455d 4x4 struggles a bit going up with both power and traction.
One gets ruts if driving on it wet.
Ok, so if I was
@Deepdrop....
I'd probably start with a rear mount brush hog or a flail on the Kioti CX2510 (which one is another discussion). Make sure the tires are set as wide as they'll go. Sometimes they can be adjusted. Also, fluid fill the rear tires. that'll help with your weight distribution.
If it is flat at the top and bottom of the hill, you can go in a circle turning in the flat area then heading back in the opposite direction.
If you can't turn around, then at first either drive forward up the hill and back down, or back up and drive forward down.
Your tractor looks like it has a pretty low center of gravity so you're probably ok even cross slope. Perhaps you could get either a center of gravity spec sheet or a cross slope rating from the manufacturer/dealer (with or without fluid in tires).
If you wish to try a zero-turn, then ask for a demo to take home and try it out with normal mowing conditions. Make sure you can mow with power going up the hill, and feel comfortable turning around.